On a Matrix Representation for Polynomially Recursive Sequences

  • Christophe Reutenauer
Keywords: p-recursive, matrix representation, Galois theory

Abstract

In this article we derive several consequences of a matricial characterization of P-recursive sequences. This characterization leads to canonical representations of these sequences. We show their uniqueness for a given sequence, up to similarity. We study their properties: operations, closed forms, d'Alembertian sequences, field extensions, positivity, extension of the sequence to $\mathbb Z$, difference Galois group.
Published
2012-09-27
Article Number
P36